## Advanced Analysis of Steel Structures

Student thesis: Master thesis (including HD thesis)

• Maria Gulbrandsen
• Rasmus Petersen
4. term, Structural and Civil Engineering, Master (Master Programme)
During the latest years, several agricultural buildings and sports arenas in Scandinavia have
collapsed due to heavy snowfalls. The loads due to a snowfall result in compression forces and
bending moments which are important factors when analysing a steel frame in the ultimate limit
state (ULS). These forces and moments can lead to global instability of the steel frame shown as
either buckling or lateral torsional buckling failure.
The European design guide Eurocode (EC) presents a number of different methods to use for an
analysis of the stability of a steel frame. Some of these methods are more simplifying than others
and therefore, the final result - the utilization ratio - is possibly affected by the method chosen for
the stability analysis of a steel frame.
This master thesis investigates the behaviour of a pinned supported reference frame constructed in
steel due to global instability. The investigation is conducted by comparing the utilization ratios
determined, respectively, by the Interaction Formulae given in Clause 6.3.3 and by the General
Method given in Clause 6.3.4 in European Standard [2005a].
The Interaction Formulae is directly determining the utilization ratio around either the y or z
axis of an element which is subjected to combined bending and axial compression. This method
takes also into account both buckling and lateral torsional buckling. The accuracy of this method
depends significantly on the assumptions made for the support conditions of the element and the
interaction factors which are based on how the moment is assumed to be distributed.
The General Method is based on the determination of two minimum load amplifiers, alpha_ult,k and
alpha_cr,op, related to the in-plane and out-of-plane behaviour of the frame, respectively. This method
allows to make use of a Finite Element Analysis to determine the two minimum load amplifiers.
The Finite Element Analyis is conducted by Abaqus/CAE, which is an engineering simulation
program.
A two-dimensional beam element model is set up for the determination of the in-plane minimum
load amplifier, alpha_ult,k, and by using that model a load-displacement curve is drawn to determine
aalpha_ult,k by the relationship between a maximum and an actual uniformly distributed line load, q_max
and q_actual, respectively. The out-of-plane minimum load amplifier, alpha_cr,op, is determined by a
three-dimensional shell element model where an eigenvalue problem is solved by a buckle analysis
performed in Abaqus/CAE. The eigenvalue, lambda_cr, related to the first out-of-plane buckling mode is
equal to the minimum load amplifier, alpha_cr,op, for the out-of-plane behaviour of the frame. These
two minimum load amplifiers are used to determine the utilization ratio by the General Method.
The utilization ratios determined by the Interaction Formulae and the General Method,
respectively, are hereafter compared to see if the methods are giving similar or different results.
In the last part of this master thesis, a parameter study is done to see what influence an effect of a
shear wall system, additional fork supports or a change of steel profile can have on the results.
Language English 7 Jun 2013 127
ID: 77336580